Using Laplace transform we have:L(x')+7L(x) = 5L(cos(2t))sL(x)-x(0) + 7L(x) = 5s/(s^2+4)(s+7)L(x)- 4 = 5s/(s^2+4)(s+7)L(x) = (5s - 4s^2 -16)/(s^2+4)
=> L(x) = -(4s^2 - 5s +16)/(s^2+4)(s+7)
now the boring part, using partial fractions we separate 1/(s^2+4)(s+7) that is:(7-s)/[53(s^2+4)] + 1/53(s+7). So:
L(x)= (1/53)[(-28s^2+4s^3-4s^2+35s-5s^2+5s)/(s^2+4) + (-4s^2+5s-16)/(s+7)]L(x)= (1/53)[(4s^3 -37s^2 +40s)/(s^2+4) + (-4s^2+5s-16)/(s+7)]
denoting T:= L^(-1)and x= (4/53) T(s^3/(s^2+4)) - (37/53)T(s^2/(s^2+4)) +(40/53) T(s^2+4)-(4/53) T(s^2/s+7) +(5/53)T(s/s+7) - (16/53) T(1/s+7)
AS we know that:

And we have the volume and we can calculate the SA,,,
So that, we can conclude:

Are you
satisfied?
The Estimated total cost was $1564. Zara do not have eough money to buy the sofa and coffee table.
<h3>What is an
equation?</h3>
An equation is an expression that shows the relationship between two or more numbers and variables.
She wants to buy a sofa for $924 and a coffee table for $640, hence:
Estimated total cost = 924 + 640 = $1564
The Estimated total cost was $1564. Zara do not have eough money to buy the sofa and coffee table.
Find out more on equation at: brainly.com/question/1214333
Answer:
The perimeter of the triangle is 
Step-by-step explanation:
Let

we know that
The perimeter of triangle is equal to

the formula to calculate the distance between two points is equal to
step 1
Find the distance AB

substitute in the formula
step 2
Find the distance BC

substitute in the formula
step 3
Find the distance AC

substitute in the formula
step 4
Find the perimeter

substitute the values

Answer:
a) Margin of error = 166.311
b) sample size ≥ 62
Step-by-step explanation:
Given:
Average cost = $1599
Sample size = 50 persons
Standard deviation = $600
Confidence level is 95%
a) Margin of error = 
Now for confidence level of 95% z-value = 1.96
Thus,
Margin of error = 
or
Margin of error = 166.311
b) For Margin of error ≤ 150
≤ 150
or
≤ 150
or
≤ √n
or
√n ≥ 7.84
or
n ≥ 61.4656
Therefore,
sample size ≥ 62